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Exchanged toric tilings, Rauzy substitution, and bounded remainder sets. (English. Russian original) Zbl 1387.11052
Math. Notes 98, No. 6, 932-948 (2015); translation from Mat. Zametki 98, No. 6, 878-897 (2015).
Summary: This paper is devoted to the two-dimensional problem of the distribution of the fractional parts of a linear function. A new class of tilings of the two-dimensional torus into bounded remainder sets with an effective estimate of the remainder is introduced. It is shown that examples of the tilings under consideration can be obtained by using the geometric version of the Rauzy substitution.

MSC:
11J71 Distribution modulo one
11H06 Lattices and convex bodies (number-theoretic aspects)
37B10 Symbolic dynamics
37B50 Multi-dimensional shifts of finite type, tiling dynamics (MSC2010)
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